DialogOS is a graphical programming environment to design computer system which can converse through voice with the user. Dialogs are clicked together in a Flowchart. DialogOS includes bindings to control Lego Mindstorms robots by voice and has bindings to SQL databases, as well as a generic plugin architecture to integrate with other types of backends. DialogOS is used in computer science courses in schools and universities to teach programming and to introduce beginners in the basic principles of human/computer interaction and dialog design. It has also been used in research systems. DialogOS was initially developed commercially by CLT Sprachtechnologie GmbH until its liquidation in 2017. The rights were then acquired by Saarland University and the software was released as open-source. == Bindings to Lego Mindstorms NXT == DialogOS can control the LEGO Mindstorms NXT Series. It uses sensor-nodes to obtain values for the following sensors: noise sensor ultrasonic sensor touch sensor luminosity sensor
International Road Traffic and Accident Database
The International Road Traffic and Accident Database (IRTAD) is an initiative dedicated to compiling and analyzing global road crash data. It is managed by the International Transport Forum (ITF) under the auspices of its permanent working group, which specializes in road safety, commonly referred to as the IRTAD Group. The primary objective of IRTAD is to provide a robust empirical basis for international comparisons in the field of road safety and to offer data to support the formulation of effective road safety policies. == Data availability == A portion of the data gathered by IRTAD is accessible for free through the OECD statistics website, however the remaining data requires a subscription for access. == History == The IRTAD database was originally started in 1988 by Germany's Federal Institution for Roads (BASt) in response to demands for international comparative data. It was later taken over and expanded by the International Transport Forum and has grown to be an important resource for comparing road safety metrics between countries worldwide, although mostly in the developed world. Every year, the ITF publishes comparative and country-by-country road safety data gathered for the IRTAD database and analysed by the IRTAD Group in the ITF Road Safety Annual Report, informally known as "IRTAD Report". Over the years, the IRTAD acronym has come to stand not only for the database, but also for the Traffic Safety Data and Analysis Group (usually referred to as IRTAD Group). The IRTAD Group is the International Transport Forum's permanent working group on road safety. It consists of a group of international road safety experts drawn from national road administrations, road safety research institutes, International organizations, automobile associations, insurance companies, car manufacturers and other road safety stakeholders. The IRTAD Group is a major forum for international road safety collaboration and exchange of best practices. Its focus is on improving road safety data as a basis for targeting interventions that are effective in reducing the number of road deaths and serious traffic injuries. The work of IRTAD, among that of others, has spawned the creation of road safety observatories for different world regions: the Ibero-American Road Safety Observatory Archived 2020-06-28 at the Wayback Machine (OISEVI), the African Road Safety Observatory Archived 2020-06-10 at the Wayback Machine, and the South-East Asian Road Safety Observatory. The ITF supports OISEVI through the Spanish-language IRTAD-LAC database and is actively involved in the implementation of the African and South East-Asian observatories. The genesis of the road safety observatory movement dates back to 2008, when the ITF, via IRTAD, began to facilitate twinning between countries striving to improve their road safety record and countries with high road safety performance. The initial twinning was between Jamaica and the United Kingdom. This work was supported by the World Bank, the Inter-American Development Bank (IADB) and the FIA Foundation. The twinning between Argentina and Spain in 2011 led to the creation of OISEVI. To this day, the ITF supports OISEVI through the Spanish-language IRTAD-LAC database. In 2006, the ITF set up Safer City Streets, a global traffic safety network for cities that replicates the successful IRTAD approach for urban road safety.
Characteristic samples
Characteristic samples is a concept in the field of grammatical inference, related to passive learning. In passive learning, an inference algorithm I {\displaystyle I} is given a set of pairs of strings and labels S {\displaystyle S} , and returns a representation R {\displaystyle R} that is consistent with S {\displaystyle S} . Characteristic samples consider the scenario when the goal is not only finding a representation consistent with S {\displaystyle S} , but finding a representation that recognizes a specific target language. A characteristic sample of language L {\displaystyle L} is a set of pairs of the form ( s , l ( s ) ) {\displaystyle (s,l(s))} where: l ( s ) = 1 {\displaystyle l(s)=1} if and only if s ∈ L {\displaystyle s\in L} l ( s ) = − 1 {\displaystyle l(s)=-1} if and only if s ∉ L {\displaystyle s\notin L} Given the characteristic sample S {\displaystyle S} , I {\displaystyle I} 's output on it is a representation R {\displaystyle R} , e.g. an automaton, that recognizes L {\displaystyle L} . == Formal Definition == === The Learning Paradigm associated with Characteristic Samples === There are three entities in the learning paradigm connected to characteristic samples, the adversary, the teacher and the inference algorithm. Given a class of languages C {\displaystyle \mathbb {C} } and a class of representations for the languages R {\displaystyle \mathbb {R} } , the paradigm goes as follows: The adversary A {\displaystyle A} selects a language L ∈ C {\displaystyle L\in \mathbb {C} } and reports it to the teacher The teacher T {\displaystyle T} then computes a set of strings and label them correctly according to L {\displaystyle L} , trying to make sure that the inference algorithm will compute L {\displaystyle L} The adversary can add correctly labeled words to the set in order to confuse the inference algorithm The inference algorithm I {\displaystyle I} gets the sample and computes a representation R ∈ R {\displaystyle R\in \mathbb {R} } consistent with the sample. The goal is that when the inference algorithm receives a characteristic sample for a language L {\displaystyle L} , or a sample that subsumes a characteristic sample for L {\displaystyle L} , it will return a representation that recognizes exactly the language L {\displaystyle L} . === Sample === Sample S {\displaystyle S} is a set of pairs of the form ( s , l ( s ) ) {\displaystyle (s,l(s))} such that l ( s ) ∈ { − 1 , 1 } {\displaystyle l(s)\in \{-1,1\}} ==== Sample consistent with a language ==== We say that a sample S {\displaystyle S} is consistent with language L {\displaystyle L} if for every pair ( s , l ( s ) ) {\displaystyle (s,l(s))} in S {\displaystyle S} : l ( s ) = 1 if and only if s ∈ L {\displaystyle l(s)=1{\text{ if and only if }}s\in L} l ( s ) = − 1 if and only if s ∉ L {\displaystyle l(s)=-1{\text{ if and only if }}s\notin L} === Characteristic sample === Given an inference algorithm I {\displaystyle I} and a language L {\displaystyle L} , a sample S {\displaystyle S} that is consistent with L {\displaystyle L} is called a characteristic sample of L {\displaystyle L} for I {\displaystyle I} if: I {\displaystyle I} 's output on S {\displaystyle S} is a representation R {\displaystyle R} that recognizes L {\displaystyle L} . For every sample D {\displaystyle D} that is consistent with L {\displaystyle L} and also fulfils S ⊆ D {\displaystyle S\subseteq D} , I {\displaystyle I} 's output on D {\displaystyle D} is a representation R {\displaystyle R} that recognizes L {\displaystyle L} . A Class of languages C {\displaystyle \mathbb {C} } is said to have charistaristic samples if every L ∈ C {\displaystyle L\in \mathbb {C} } has a characteristic sample. == Related Theorems == === Theorem === If equivalence is undecidable for a class C {\textstyle \mathbb {C} } over Σ {\textstyle \Sigma } of cardinality bigger than 1, then C {\textstyle \mathbb {C} } doesn't have characteristic samples. ==== Proof ==== Given a class of representations C {\textstyle \mathbb {C} } such that equivalence is undecidable, for every polynomial p ( x ) {\displaystyle p(x)} and every n ∈ N {\displaystyle n\in \mathbb {N} } , there exist two representations r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} of sizes bounded by n {\displaystyle n} , that recognize different languages but are inseparable by any string of size bounded by p ( n ) {\displaystyle p(n)} . Assuming this is not the case, we can decide if r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} are equivalent by simulating their run on all strings of size smaller than p ( n ) {\displaystyle p(n)} , contradicting the assumption that equivalence is undecidable. === Theorem === If S 1 {\displaystyle S_{1}} is a characteristic sample for L 1 {\displaystyle L_{1}} and is also consistent with L 2 {\displaystyle L_{2}} , then every characteristic sample of L 2 {\displaystyle L_{2}} , is inconsistent with L 1 {\displaystyle L_{1}} . ==== Proof ==== Given a class C {\textstyle \mathbb {C} } that has characteristic samples, let R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} be representations that recognize L 1 {\displaystyle L_{1}} and L 2 {\displaystyle L_{2}} respectively. Under the assumption that there is a characteristic sample for L 1 {\displaystyle L_{1}} , S 1 {\displaystyle S_{1}} that is also consistent with L 2 {\displaystyle L_{2}} , we'll assume falsely that there exist a characteristic sample for L 2 {\displaystyle L_{2}} , S 2 {\displaystyle S_{2}} that is consistent with L 1 {\displaystyle L_{1}} . By the definition of characteristic sample, the inference algorithm I {\displaystyle I} must return a representation which recognizes the language if given a sample that subsumes the characteristic sample itself. But for the sample S 1 ∪ S 2 {\displaystyle S_{1}\cup S_{2}} , the answer of the inferring algorithm needs to recognize both L 1 {\displaystyle L_{1}} and L 2 {\displaystyle L_{2}} , in contradiction. === Theorem === If a class is polynomially learnable by example based queries, it is learnable with characteristic samples. == Polynomialy characterizable classes == === Regular languages === The proof that DFA's are learnable using characteristic samples, relies on the fact that every regular language has a finite number of equivalence classes with respect to the right congruence relation, ∼ L {\displaystyle \sim _{L}} (where x ∼ L y {\displaystyle x\sim _{L}y} for x , y ∈ Σ ∗ {\displaystyle x,y\in \Sigma ^{}} if and only if ∀ z ∈ Σ ∗ : x z ∈ L ↔ y z ∈ L {\displaystyle \forall z\in \Sigma ^{}:xz\in L\leftrightarrow yz\in L} ). Note that if x {\displaystyle x} , y {\displaystyle y} are not congruent with respect to ∼ L {\displaystyle \sim _{L}} , there exists a string z {\displaystyle z} such that x z ∈ L {\displaystyle xz\in L} but y z ∉ L {\displaystyle yz\notin L} or vice versa, this string is called a separating suffix. ==== Constructing a characteristic sample ==== The construction of a characteristic sample for a language L {\displaystyle L} by the teacher goes as follows. Firstly, by running a depth first search on a deterministic automaton A {\displaystyle A} recognizing L {\displaystyle L} , starting from its initial state, we get a suffix closed set of words, W {\displaystyle W} , ordered in shortlex order. From the fact above, we know that for every two states in the automaton, there exists a separating suffix that separates between every two strings that the run of A {\displaystyle A} on them ends in the respective states. We refer to the set of separating suffixes as S {\displaystyle S} . The labeled set (sample) of words the teacher gives the adversary is { ( w , l ( w ) ) | w ∈ W ⋅ S ∪ W ⋅ Σ ⋅ S } {\displaystyle \{(w,l(w))|w\in W\cdot S\cup W\cdot \Sigma \cdot S\}} where l ( w ) {\displaystyle l(w)} is the correct label of w {\displaystyle w} (whether it is in L {\displaystyle L} or not). We may assume that ϵ ∈ S {\displaystyle \epsilon \in S} . ==== Constructing a deterministic automata ==== Given the sample from the adversary W {\displaystyle W} , the construction of the automaton by the inference algorithm I {\displaystyle I} starts with defining P = prefix ( W ) {\displaystyle P={\text{prefix}}(W)} and S = suffix ( W ) {\displaystyle S={\text{suffix}}(W)} , which are the set of prefixes and suffixes of W {\displaystyle W} respectively. Now the algorithm constructs a matrix M {\displaystyle M} where the elements of P {\displaystyle P} function as the rows, ordered by the shortlex order, and the elements of S {\displaystyle S} function as the columns, ordered by the shortlex order. Next, the cells in the matrix are filled in the following manner for prefix p i {\displaystyle p_{i}} and suffix s j {\displaystyle s_{j}} : If p i s j ∈ W → M i j = l ( p i s j ) {\displaystyle p_{i}s_{j}\in W\rightarrow M_{ij}=l(p_{i}s_{j})} else, M i j = 0 {\displaystyle M_{ij}=0} Now, we say row i {\displaystyle i} and t {\displaystyle t} are distinguishable if there exi
Iris flower data set
The Iris flower data set or Fisher's Iris data set is a multivariate data set used and made famous by the British statistician and biologist Ronald Fisher in his 1936 paper The use of multiple measurements in taxonomic problems as an example of linear discriminant analysis. It is sometimes called Anderson's Iris data set because Edgar Anderson collected the data to quantify the morphologic variation of Iris flowers of three related species. Two of the three species were collected in the Gaspé Peninsula "all from the same pasture, and picked on the same day and measured at the same time by the same person with the same apparatus". The data set consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor). Four features were measured from each sample: the length and the width of the sepals and petals, in centimeters. Based on the combination of these four features, Fisher developed a linear discriminant model to distinguish each species. Fisher's paper was published in the Annals of Eugenics (today the Annals of Human Genetics). == Use of the data set == Originally used as an example data set on which Fisher's linear discriminant analysis was applied, it became a typical test case for many statistical classification techniques in machine learning such as support vector machines. The use of this data set in cluster analysis however is not common, since the data set only contains two clusters with rather obvious separation. One of the clusters contains Iris setosa, while the other cluster contains both Iris virginica and Iris versicolor and is not separable without the species information Fisher used. This makes the data set a good example to explain the difference between supervised and unsupervised techniques in data mining: Fisher's linear discriminant model can only be obtained when the object species are known: class labels and clusters are not necessarily the same. Nevertheless, all three species of Iris are separable in the projection on the nonlinear and branching principal component. The data set is approximated by the closest tree with some penalty for the excessive number of nodes, bending and stretching. Then the so-called "metro map" is constructed. The data points are projected into the closest node. For each node the pie diagram of the projected points is prepared. The area of the pie is proportional to the number of the projected points. It is clear from the diagram (left) that the absolute majority of the samples of the different Iris species belong to the different nodes. Only a small fraction of Iris-virginica is mixed with Iris-versicolor (the mixed blue-green nodes in the diagram). Therefore, the three species of Iris (Iris setosa, Iris virginica and Iris versicolor) are separable by the unsupervising procedures of nonlinear principal component analysis. To discriminate them, it is sufficient just to select the corresponding nodes on the principal tree. == Data set == The data set contains a set of 150 records under five attributes: sepal length, sepal width, petal length, petal width and species. The iris data set is widely used as a beginner's data set for machine learning purposes. The data set is included in R base and Python in the machine learning library scikit-learn, so that users can access it without having to find a source for it. Several versions of the data set have been published. === R code illustrating usage === The example R code shown below reproduce the scatterplot displayed at the top of this article: === Python code illustrating usage === This code gives:
Alternating decision tree
An alternating decision tree (ADTree) is a machine learning method for classification. It generalizes decision trees and has connections to boosting. An ADTree consists of an alternation of decision nodes, which specify a predicate condition, and prediction nodes, which contain a single number. An instance is classified by an ADTree by following all paths for which all decision nodes are true, and summing any prediction nodes that are traversed. == History == ADTrees were introduced by Yoav Freund and Llew Mason. However, the algorithm as presented had several typographical errors. Clarifications and optimizations were later presented by Bernhard Pfahringer, Geoffrey Holmes and Richard Kirkby. Implementations are available in Weka and JBoost. == Motivation == Original boosting algorithms typically used either decision stumps or decision trees as weak hypotheses. As an example, boosting decision stumps creates a set of T {\displaystyle T} weighted decision stumps (where T {\displaystyle T} is the number of boosting iterations), which then vote on the final classification according to their weights. Individual decision stumps are weighted according to their ability to classify the data. Boosting a simple learner results in an unstructured set of T {\displaystyle T} hypotheses, making it difficult to infer correlations between attributes. Alternating decision trees introduce structure to the set of hypotheses by requiring that they build off a hypothesis that was produced in an earlier iteration. The resulting set of hypotheses can be visualized in a tree based on the relationship between a hypothesis and its "parent." Another important feature of boosted algorithms is that the data is given a different distribution at each iteration. Instances that are misclassified are given a larger weight while accurately classified instances are given reduced weight. == Alternating decision tree structure == An alternating decision tree consists of decision nodes and prediction nodes. Decision nodes specify a predicate condition. Prediction nodes contain a single number. ADTrees always have prediction nodes as both root and leaves. An instance is classified by an ADTree by following all paths for which all decision nodes are true and summing any prediction nodes that are traversed. This is different from binary classification trees such as CART (Classification and regression tree) or C4.5 in which an instance follows only one path through the tree. === Example === The following tree was constructed using JBoost on the spambase dataset (available from the UCI Machine Learning Repository). In this example, spam is coded as 1 and regular email is coded as −1. The following table contains part of the information for a single instance. The instance is scored by summing all of the prediction nodes through which it passes. In the case of the instance above, the score is calculated as The final score of 0.657 is positive, so the instance is classified as spam. The magnitude of the value is a measure of confidence in the prediction. The original authors list three potential levels of interpretation for the set of attributes identified by an ADTree: Individual nodes can be evaluated for their own predictive ability. Sets of nodes on the same path may be interpreted as having a joint effect The tree can be interpreted as a whole. Care must be taken when interpreting individual nodes as the scores reflect a re weighting of the data in each iteration. == Description of the algorithm == The inputs to the alternating decision tree algorithm are: A set of inputs ( x 1 , y 1 ) , … , ( x m , y m ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{m},y_{m})} where x i {\displaystyle x_{i}} is a vector of attributes and y i {\displaystyle y_{i}} is either -1 or 1. Inputs are also called instances. A set of weights w i {\displaystyle w_{i}} corresponding to each instance. The fundamental element of the ADTree algorithm is the rule. A single rule consists of a precondition, a condition, and two scores. A condition is a predicate of the form "attribute
AlphaChip (controversy)
The AlphaChip controversy refers to a series of public, scholarly, and legal disputes surrounding a 2021 Nature paper by Google-affiliated researchers. The paper describes an approach to macro placement, a stage of chip floorplanning, based on reinforcement learning (RL), a machine learning method in which a system iteratively improves its decisions by optimizing performance-based reward signals. The primary technical question is whether the new techniques are better than existing (non-AI) techniques. Both internal Google studies and external attempts to replicate the algorithm have failed to show the claimed benefits. No head-to-head comparison is available because the data used in the paper is proprietary, and Google has not released any results from running its algorithm on public benchmarks. This has resulted in considerable skepticism over the paper's claims. In addition, the inability of others (both inside and outside of Google) to replicate the claimed results have sparked concerns about the paper’s methodology, reproducibility, and scientific integrity. The lead researchers of the Nature paper were affiliated with Google Brain, which became part of Google DeepMind, and later spun off into the company Ricursive. == Motivation for research: Macro placement in chip layout == Chip design for modern integrated circuits is a complex, expert-driven process that relies on electronic design automation. It determines the performance of the final chip, and takes weeks or months to complete. Advances that produce better designs, or complete the process faster, are commercially and academically significant. Macro placement is a step during chip design that determines the locations of large circuit components (macros) within a chip. It is followed by detailed placement, which places the far more numerous but much smaller standard cells. Alternatively, mixed-size placement simultaneously places both large macros and millions of small cells, requiring algorithms to handle objects that differ by several orders of magnitude in area and mobility. The number of macros per circuit typically ranges from several to thousands. Wiring must be performed after placement, and the details of this wiring strongly influence the power, performance, and area (PPA) of the completed chip. The full wiring calculation is very resource intensive, so placement tools typically use a proxy cost, a simplified objective function used to guide the placement algorithm during training and evaluation. The faithfulness of the chosen proxy cost to the final objective cost is a critical aspect of placer performance. === State of the art as of 2021 === Chips have been designed since the 1960s, so there were many existing methods as of 2021. Available options included manual design, academic tools, and commercial offerings. Academic methods include combinatorial optimization techniques such as simulated annealing, analytical placement, hierarchical heuristics, and as of 2019 reinforcement learning and broader machine learning techniques.. Existing (non-AI) academic tools for solving the same problem include APlace, NTUplace3, ePlace, RePlace, and DREAMPlace. Commercial EDA vendors also offered automated software tools for floorplanning and mixed-size placement. For instance, as of 2019 Cadence’s Innovus implementation software offered a Concurrent Macro Placer (CMP) feature to automatically place large blocks and standard cells. == The 2021 Nature paper and its claims == In 2021, Nature published a paper under the title “A graph‑placement methodology for fast chip design” co‑authored by 21 Google-affiliated researchers. The paper reported that an RL agent could generate macro placements for integrated circuits "in under six hours" and achieve improvements over human-designed layouts in power, timing performance, and area (PPA), standard chip-quality metrics referring respectively to energy consumption, chip operating speed, and silicon footprint (evaluated after wire routing). It introduced a sequential macro placement algorithm in which macros are placed one at a time instead of optimizing their locations concurrently. At each step, the algorithm selects a location for a single macro on a discretized chip canvas, conditioning its decision on the placements of previously placed macros. This sequential formulation converts macro placement into a long-horizon decision process in which early placement choices constrain later ones. After macro placement, force-directed placement is applied to place standard cells connected to the macros. Deep reinforcement learning is used to train a policy network to place macros by maximizing a reward that reflects final placement quality (for example, wirelength and congestion). Policy learning occurs during self‑play for one or multiple circuit designs. Further placement optimizations refine the overall layout by balancing wirelength, density, and overlap constraints, while treating the macro locations produced by the RL policy as fixed obstacles. The approach relies on pre-training, in which the RL model is first trained on a corpus of prior designs (twenty in the Nature paper) to learn general placement patterns before being fine-tuned on a specific chip. Circuit examples used in the study were parts of proprietary Google TPU designs, called blocks (or floorplan partitions). The paper reported results on five blocks and described the approach as generalizable across chip designs. == Controversy == Soon after the paper's publication, controversy arose over whether the claims were true, whether they were sufficiently proven, and whether academic standards were followed. These controversies arose both within Google and among external academic experts. === Internal dispute at Google and legal proceedings === In 2022, Satrajit Chatterjee, a Google engineer involved in reviewing the AlphaChip work, raised concerns internally and drafted an alternative analysis, (Stronger Baselines) arguing that established methods outperformed the RL approach under fair comparison. In March 2022, Google declined to publish this analysis and terminated Chatterjee's employment. Chatterjee filed a wrongful dismissal lawsuit, alleging that representations related to the AlphaChip research involved fraud and scientific misconduct. According to court documents, Chatterjee's study was conducted "in the context of a large potential Google Cloud deal". He noted that it "would have been unethical to imply that we had revolutionary technology when our tests showed otherwise" and claimed Google was deliberately withholding material information. Furthermore, the committee that reviewed his paper and disapproved its publication was allegedly chaired by subordinates of Jeff Dean, a senior co-author of the Nature paper. Google’s subsequent motion to dismiss was denied, holding that Chatterjee had plausibly alleged retaliation for refusing to engage in conduct he believed would violate state or federal law. === External controversy === The external questions can be summarized in four main points: (a) Are the claims supported by the evidence provided? (b) Did the paper provide enough information to allow the results to be independently reproduced and verified? If so, are the results an improvement over existing academic and commercial tools? (c) Were the comparisons in the paper done fairly and with full disclosure? (d) Were academic standards followed? Each of these is discussed below. ==== Are the claims supported by the evidence provided? ==== The Nature paper described the reduction in design-process time as going from "days or weeks" to "hours", but did not provide per-design time breakdowns or specify the number of engineers, their level of expertise, or the baseline tools and workflow against which this comparison was made. It was also unclear whether the "days or weeks" baseline included time spent on other tasks such as functional design changes. The paper also evaluated the method on fewer benchmarks (five) than is common in the field, and showed mixed results across different evaluation goals While the approach was described as improving circuit area, this claim seems unsupported, as the RL optimization did not alter the overall circuit area, as it adjusted only the locations of fixed-shape non-overlapping circuit components within a fixed rectangular layout boundary. ==== Comparison with existing methods, and replicating the algorithm ==== Because macro placement is largely geometric and its fundamental algorithms are not tied to a specific process node, competing approaches can be evaluated on public benchmarks (tests) across technologies, rather than primarily on proprietary internal designs. This is standard procedure when comparing academic placers, see . In contrast, Google has only reported results only on internal proprietary designs, and as of 2026 has not offered comparisons with prior methods on common benchmarks. Researchers at the University of Califor
Averaged one-dependence estimators
Averaged one-dependence estimators (AODE) is a probabilistic classification learning technique. It was developed to address the attribute-independence problem of the popular naive Bayes classifier. It frequently develops substantially more accurate classifiers than naive Bayes at the cost of a modest increase in the amount of computation. == The AODE classifier == AODE seeks to estimate the probability of each class y given a specified set of features x1, ... xn, P(y | x1, ... xn). To do so it uses the formula P ^ ( y ∣ x 1 , … x n ) = ∑ i : 1 ≤ i ≤ n ∧ F ( x i ) ≥ m P ^ ( y , x i ) ∏ j = 1 n P ^ ( x j ∣ y , x i ) ∑ y ′ ∈ Y ∑ i : 1 ≤ i ≤ n ∧ F ( x i ) ≥ m P ^ ( y ′ , x i ) ∏ j = 1 n P ^ ( x j ∣ y ′ , x i ) {\displaystyle {\hat {P}}(y\mid x_{1},\ldots x_{n})={\frac {\sum _{i:1\leq i\leq n\wedge F(x_{i})\geq m}{\hat {P}}(y,x_{i})\prod _{j=1}^{n}{\hat {P}}(x_{j}\mid y,x_{i})}{\sum _{y^{\prime }\in Y}\sum _{i:1\leq i\leq n\wedge F(x_{i})\geq m}{\hat {P}}(y^{\prime },x_{i})\prod _{j=1}^{n}{\hat {P}}(x_{j}\mid y^{\prime },x_{i})}}} where P ^ ( ⋅ ) {\displaystyle {\hat {P}}(\cdot )} denotes an estimate of P ( ⋅ ) {\displaystyle P(\cdot )} , F ( ⋅ ) {\displaystyle F(\cdot )} is the frequency with which the argument appears in the sample data and m is a user specified minimum frequency with which a term must appear in order to be used in the outer summation. In recent practice m is usually set at 1. == Derivation of the AODE classifier == We seek to estimate P(y | x1, ... xn). By the definition of conditional probability P ( y ∣ x 1 , … x n ) = P ( y , x 1 , … x n ) P ( x 1 , … x n ) . {\displaystyle P(y\mid x_{1},\ldots x_{n})={\frac {P(y,x_{1},\ldots x_{n})}{P(x_{1},\ldots x_{n})}}.} For any 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n} , P ( y , x 1 , … x n ) = P ( y , x i ) P ( x 1 , … x n ∣ y , x i ) . {\displaystyle P(y,x_{1},\ldots x_{n})=P(y,x_{i})P(x_{1},\ldots x_{n}\mid y,x_{i}).} Under an assumption that x1, ... xn are independent given y and xi, it follows that P ( y , x 1 , … x n ) = P ( y , x i ) ∏ j = 1 n P ( x j ∣ y , x i ) . {\displaystyle P(y,x_{1},\ldots x_{n})=P(y,x_{i})\prod _{j=1}^{n}P(x_{j}\mid y,x_{i}).} This formula defines a special form of One Dependence Estimator (ODE), a variant of the naive Bayes classifier that makes the above independence assumption that is weaker (and hence potentially less harmful) than the naive Bayes' independence assumption. In consequence, each ODE should create a less biased estimator than naive Bayes. However, because the base probability estimates are each conditioned by two variables rather than one, they are formed from less data (the training examples that satisfy both variables) and hence are likely to have more variance. AODE reduces this variance by averaging the estimates of all such ODEs. == Features of the AODE classifier == Like naive Bayes, AODE does not perform model selection and does not use tuneable parameters. As a result, it has low variance. It supports incremental learning whereby the classifier can be updated efficiently with information from new examples as they become available. It predicts class probabilities rather than simply predicting a single class, allowing the user to determine the confidence with which each classification can be made. Its probabilistic model can directly handle situations where some data are missing. AODE has computational complexity O ( l n 2 ) {\displaystyle O(ln^{2})} at training time and O ( k n 2 ) {\displaystyle O(kn^{2})} at classification time, where n is the number of features, l is the number of training examples and k is the number of classes. This makes it infeasible for application to high-dimensional data. However, within that limitation, it is linear with respect to the number of training examples and hence can efficiently process large numbers of training examples. == Implementations == The free Weka machine learning suite includes an implementation of AODE.